Remark on "When Are All the Zeros of a Polynomial Real and Distinct?"

TL;DR

This note highlights that a key result about the reality and distinctness of polynomial zeros is already known within the elementary theory of orthogonal polynomials, emphasizing its implicit presence in existing mathematical literature.

Contribution

It clarifies that the main theorem of the referenced paper is not new but is implicitly contained in well-established orthogonal polynomial theory.

Findings

The main result is part of elementary orthogonal polynomial theory.

No new proof or result is introduced.

The result is well-known in the mathematical community.

Abstract

The purpose of this note is to point out that the main result of [M. Chamberland, When Are All the Zeros of a Polynomial Real and Distinct? Amer. Math. Monthly. 127 (2020) 449-451] is implicitly contained in the elementary lore of the theory of orthogonal polynomials on the real line.